T.rho {LongMemoryTS}

Test for equality of all elements in an estimated d-vector based on pairwise comparisons.

Description

T.rho Uses pairwise test as suggested by Robinson and Yajima (2002) to test for the equality of the memory parameters in a vector series.

Usage

T.rho(data, d.hat, m, m1, alpha = 0.05, s_bar = 1,
  h_n = 1/sqrt(log(max(dim(data)))))

Arguments

data

data matrix of dimension (qxT).

d.hat

the estimated d.vector

m

bandwith parameter specifying the number of Fourier frequencies. used for the estimation of G, usually floor(1+T^delta), where 0<delta<1.

m1

the bandwidth parameter used for estimation of d.vec with m1>>m

alpha

the desired significance level for the tests

s_bar

number of subvectors to be tested in partitioning procedure. Default is s_bar=1, for independent use.

h_n

bandwidth parameter. Default is h_n=1/sqrt(log(max(dim(data)))) which is recommended by Nielsen and Shimotsu (2007) in their simulation study. Robinson and Yajima (2002) argue non-rejection with h_n=0 would imply non-rejection with any h_n>0.

Author(s)

Christian Leschinski

References

Robinson, P. M. and Yajima, Y. (2002): Determination of cointegrating rank in fractional systems. Journal of Econometrics, Vol. 106, No.2, pp. 217-241.

Nielsen, M. O. and Shimotsu, K. (2007): Determining the coinegrating rank in nonstationary fractional systems by the exact local Whittle approach. Journal of Econometrics, 141, pp. 574-596.

Examples

library(fracdiff)
T<-1000
d1<-0.2
d2<-0.4
X<-cbind(fracdiff.sim(n=T,d=d1)$series,fracdiff.sim(n=T,d=d1)$series,
fracdiff.sim(n=T,d=d2)$series,fracdiff.sim(n=T,d=d2)$series)
alpha<-0.05
m1<-floor(1+T^0.75)
m<-floor(1+T^0.65)
lW.wrap<-function(data,m){local.W(data,m)$d}
d.hat<-apply(X,2,lW.wrap, m=m1)
T.rho(data=X, d.hat=d.hat, m=m, m1=m1)